Abstract

The English Premier League has seen a noticeable rise in US viewership over recent years - contributing to the already wide scale popularity of the sport. No matter the sport, refereeing seems to be a major speaking point across fan bases whether that be the call inconsistencies, missed calls, or speculative fouls. The purpose of this report and analyses is to understand whether there is an inconsistency in refereeing and whether or not it has a significant impact on the result of any given match - although this goal pivoted slightly during the model creation process.

Methodology

The model creation process in this report started the final_dataset.csv file dowloaded from Kaggle.com with variables regarding Home/Away team, total booking points, Away/Home Cards, Referee, etc. Using this data we generated some variables seen on the EPL_New.csv some of these are Predicted Outcome Success (POS), Expected Result (ExpectedR), Expected Result Odds (ERO), Home/Away/Total Booking Points (HBP,ABP,TBP). Other variables that were taken into consideration were Bet365 Closing Odds (B365CH & B365CA).

POS and ExpectedR were both treated as binary variables. Although in english football matches can result in a draw - bookies release closing odds based on whether a team wins or losings. Fitting a logistic regression model with a draw wouldn’t make much sense.

This report contains initial data analysis and exploration, logistic regression, Lasso variable selection and model prediction. The analyses and visualizations done within this report was created with a combination of RStudio, Jamovi, Jupyter Lab.

Discussion

Initially the question we wanted to answer was did booking points - points calculated by yellow/red cards given during the match - significantly impacted a match’s outcome. Following this curiosity we wanted to know if there was consistency between the yellow/red cards given throughout a game and the referee’s issuing them.

Since red cards issuance is rare in the sport it’s to no surprise that the density plots show that most referees don’t issue red cards much - this was expected given what we know. It is worth noting that some referee’s density at one red card given stood out though, for example Graham Scott and Paul Tierney.

This photo depicts the differences between referees and their yellow card issuance rate. We noticed that yellow card issuance (on a game-to-game basis) highly varied between referees. This visualization peaked our interest and sparked our initial research question. We figured that there was going to be variability between referees; however, we didn’t expect this much variable among yellow card issuance.

Just for further confirmation, we then wanted to run an ANOVA model to see if we really had a significant difference in means across referees, this would eliminate any worries of certaing referees officiating more or less matches than others. When choosing the variable to run ANOVA on - we realized we wanted to grasp a referees’ card impact through one variable, total booking points. This is a computed variable that football-data.co.uk (the original source of the data) mentions on their website; It gives each yellow card per match a value of 10 points, and a red card 25 points. For the situation in which a player received a red card through two yellow cards, the first yellow card was counted as 10 points, while the second was just counted as a red card, 25 points. Back to our ANOVA model, the p-value for referees was < 0.00001. This tells us that referees impact on total booking points per game is statistically significant and can be attributed to individual referee’s decision-making.

Continuing our in our exploratory process we wanted to take a closer look at booking points through a couple of models made in Jupyter Lab.